Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the mass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement invetvals (FIA re-measurment period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.

Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(G\) with increasing \(B\), thus, weighted nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {mean B_{t1}}\) in equal-sample sized plot biomass bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.

Model selection is used to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:

model 1: simple model \(G = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 2: phi model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

model 3: phi-alpha model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)

Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)

sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)

NOTE:

This document contains all \(G\) observations that meet our plot-based filtering criteria:

exclude FIA plots in plantation forests
exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile thresholding approach. We also calculated plot \(G_{TI}\) using as summed tree incremental growth for all trees > 12.5 cm (5 inches) (see supplementary methods). We use the difference between the two methods, which we define \(diff_G\) as the difference between the two methods \(G_{MB} - G_{TI}\) to identify erroneous or outlier growth calculations. We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1760 observations.

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6822     6736.7                                 
## 2   6821     6721.5  1  15.195   15.42 8.693e-05 ***
## 3   6820     6431.3  1 290.282  307.83 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 27051.87
## 2     2 27038.46
## 3     3 26739.15

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.009888   0.165037  -0.060    0.952    
## phi    0.019998   0.005047   3.963 7.49e-05 ***
## alpha  0.634061   0.033868  18.721  < 2e-16 ***
## A      3.581300   0.119640  29.934  < 2e-16 ***
## k      6.522308   0.615369  10.599  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9711 on 6820 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.129e-06
##   (52 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   6820     6431.3                              
## 2   6819     6422.8  1 8.4735  8.9962 0.002715 **
## 3   6819     6424.1  0 0.0000                    
## 4   6818     6422.7  1 1.3373  1.4196 0.233510   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 26739.15
## 2    3a 26732.16
## 3    3b 26733.53
## 4    3c 26734.11

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.010980   0.164841  -0.067 0.946895    
## phi    0.020140   0.005047   3.991 6.66e-05 ***
## alpha  0.632787   0.033845  18.696  < 2e-16 ***
## A      3.649991   0.126777  28.791  < 2e-16 ***
## k     11.607027   2.534980   4.579 4.76e-06 ***
## p      0.243508   0.068055   3.578 0.000349 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9705 on 6819 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 2.248e-06
##   (52 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 17 rows containing missing values (geom_point).

## Warning: Removed 1038 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1  18911      20242                                  
## 2  18906      20178  5   64.05   12.002 1.264e-11 ***
## 3  18905      19036  1 1142.81 1134.976 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 70366.34
## 2     2 70297.09
## 3     3 69196.58

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.999943   0.163099   6.131 8.91e-10 ***
## phi    0.025881   0.003152   8.211 2.34e-16 ***
## alpha  0.806838   0.021956  36.748  < 2e-16 ***
## A      2.599578   0.070225  37.018  < 2e-16 ***
## k     10.057721   0.453530  22.177  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.003 on 18905 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.524e-06
##   (3805 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  18905      19036                                 
## 2  18904      18862  1 173.649 174.037 < 2.2e-16 ***
## 3  18904      18877  0   0.000                      
## 4  18903      18860  1  17.168  17.208 3.365e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 69196.58
## 2    3a 69025.29
## 3    3b 69040.25
## 4    3c 69025.04

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.954318   0.159882   5.969 2.43e-09 ***
## phi    0.026434   0.003124   8.461  < 2e-16 ***
## alpha  0.799224   0.021796  36.669  < 2e-16 ***
## A      2.982149   0.151152  19.729  < 2e-16 ***
## k     25.323669   2.936663   8.623  < 2e-16 ***
## p      0.189430   0.033063   5.729 1.02e-08 ***
## s      0.840369   0.096756   8.685  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9989 on 18903 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.558e-06
##   (3805 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1926 rows containing missing values (geom_point).

## Warning: Removed 1031 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7266      10676                                
## 2   7265      10653  1  22.84  15.577 7.997e-05 ***
## 3   7264      10214  1 438.37 311.752 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 32681.15
## 2     2 32667.58
## 3     3 32364.13

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.924852   0.125834  -7.350  2.2e-13 ***
## phi    0.019083   0.005448   3.503 0.000464 ***
## alpha  0.750989   0.039859  18.841  < 2e-16 ***
## A      5.243628   0.171545  30.567  < 2e-16 ***
## k     14.164894   1.593463   8.889  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.186 on 7264 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.323e-06
##   (64 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7264      10214                                
## 2   7263      10127  1 86.861  62.294 3.393e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 32364.13
## 2    3a 32304.05
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.991815   0.121470  -8.165 3.76e-16 ***
## phi     0.020466   0.005431   3.768 0.000166 ***
## alpha   0.745886   0.039181  19.037  < 2e-16 ***
## A       7.709358   0.830328   9.285  < 2e-16 ***
## k     215.668276  75.532860   2.855 0.004312 ** 
## p       0.378545   0.029251  12.941  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.181 on 7263 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 5.564e-06
##   (64 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 32 rows containing missing values (geom_point).

## Warning: Removed 1036 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1   4839     6092.2                                  
## 2   4838     6083.5  1   8.735   6.9469  0.008423 ** 
## 3   4837     5798.3  1 285.221 237.9360 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 20152.37
## 2     2 20147.42
## 3     3 19916.91

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.165710   0.234835  -0.706   0.4804    
## phi    0.021579   0.009282   2.325   0.0201 *  
## alpha  0.774996   0.045980  16.855   <2e-16 ***
## A      4.302197   0.195800  21.972   <2e-16 ***
## k     18.366586   1.551671  11.837   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.095 on 4837 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.64e-06
##   (1003 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4837     5798.3                                
## 2   4836     5686.0  1 112.22  95.442 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 19916.91
## 2    3a 19824.28
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.201434   0.229034  -0.879   0.3792    
## phi     0.017214   0.009048   1.902   0.0572 .  
## alpha   0.756562   0.045588  16.596  < 2e-16 ***
## A       6.225883   0.495601  12.562  < 2e-16 ***
## k     125.317993  25.375248   4.939 8.13e-07 ***
## p       0.250791   0.015405  16.280  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.084 on 4836 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 5.288e-06
##   (1003 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 489 rows containing missing values (geom_point).

## Warning: Removed 1053 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   8742      11815                                
## 2   8741      11811  1   3.813   2.8219 0.09302 .  
## 3   8740      11530  1 280.812 212.8594 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 36909.11
## 2     2 36908.29
## 3     3 36699.86

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.678595   0.137007  -4.953 7.44e-07 ***
## phi   -0.012357   0.006662  -1.855   0.0637 .  
## alpha  0.667559   0.042864  15.574  < 2e-16 ***
## A      4.813998   0.167516  28.738  < 2e-16 ***
## k     27.676460   2.451572  11.289  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.149 on 8740 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 7.363e-06
##   (1265 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     3 36699.86
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.678595   0.137007  -4.953 7.44e-07 ***
## phi   -0.012357   0.006662  -1.855   0.0637 .  
## alpha  0.667559   0.042864  15.574  < 2e-16 ***
## A      4.813998   0.167516  28.738  < 2e-16 ***
## k     27.676460   2.451572  11.289  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.149 on 8740 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 7.363e-06
##   (1265 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 620 rows containing missing values (geom_point).

## Warning: Removed 1002 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq   F value Pr(>F)    
## 1  13233      32413                               
## 2  13232      32401  1   12.0    4.8986 0.0269 *  
## 3  13231      29228  1 3172.8 1436.2611 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69085.33
## 2     2 69082.43
## 3     3 67720.39

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    1.102065   0.172012   6.407 1.54e-10 ***
## phi   0.004936   0.004586   1.076    0.282    
## alpha 0.868963   0.020677  42.026  < 2e-16 ***
## A     4.273767   0.121223  35.255  < 2e-16 ***
## k     1.136799   0.159419   7.131 1.05e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.486 on 13231 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.937e-06
##   (281 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_231,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13231      29228                                
## 2  13230      29132  1 96.472  43.812 3.754e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 67720.39
## 2    3a 67678.63
## 3    3b 67680.30
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    1.048665   0.169018   6.204 5.65e-10 ***
## phi   0.005156   0.004571   1.128 0.259335    
## alpha 0.868886   0.020547  42.288  < 2e-16 ***
## A     4.439114   0.131521  33.752  < 2e-16 ***
## k     7.625377   2.249531   3.390 0.000702 ***
## p     0.531025   0.050814  10.450  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.484 on 13230 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.12e-06
##   (281 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 143 rows containing missing values (geom_point).

## Warning: Removed 1017 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq   F value Pr(>F)    
## 1  13303      36087                               
## 2  13302      36072  1   15.2    5.5979  0.018 *  
## 3  13301      32458  1 3613.9 1480.9394 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69162.02
## 2     2 69158.42
## 3     3 67755.75

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.779744   0.174483   4.469 7.93e-06 ***
## phi   0.005289   0.004831   1.095    0.274    
## alpha 0.870086   0.020029  43.441  < 2e-16 ***
## A     4.431463   0.138940  31.895  < 2e-16 ***
## k     5.232230   0.410294  12.752  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.562 on 13301 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.162e-06
##   (323 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  13301      32458                                 
## 2  13300      32149  1 308.467 127.611 < 2.2e-16 ***
## 3  13300      32173  0   0.000                      
## 4  13299      32149  1  24.192  10.008  0.001562 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 67755.75
## 2    3a 67630.69
## 3    3b 67640.55
## 4    3c 67632.54

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.699821   0.168755   4.147 3.39e-05 ***
## phi    0.004628   0.004787   0.967    0.334    
## alpha  0.865348   0.019874  43.543  < 2e-16 ***
## A      4.879788   0.167465  29.139  < 2e-16 ***
## k     24.840494   3.992074   6.222 5.04e-10 ***
## p      0.399310   0.024277  16.448  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.555 on 13300 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.829e-06
##   (323 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 169 rows containing missing values (geom_point).

## Warning: Removed 931 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1324     3607.2                              
## 2   1323     3606.2  1   0.949  0.3483 0.5552    
## 3   1322     3405.6  1 200.621 77.8782 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6965.867
## 2     2 6967.518
## 3     3 6893.561

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.90809    1.29228   1.477   0.1400    
## phi   -0.02371    0.02173  -1.091   0.2754    
## alpha  0.80459    0.08194   9.820  < 2e-16 ***
## A      3.54620    0.68006   5.215 2.14e-07 ***
## k      4.45195    1.57213   2.832   0.0047 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.605 on 1322 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 6.242e-06
##   (61 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 6893.561
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.90809    1.29228   1.477   0.1400    
## phi   -0.02371    0.02173  -1.091   0.2754    
## alpha  0.80459    0.08194   9.820  < 2e-16 ***
## A      3.54620    0.68006   5.215 2.14e-07 ***
## k      4.45195    1.57213   2.832   0.0047 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.605 on 1322 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 6.242e-06
##   (61 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91821, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.7387, p-value = 0.000185
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 27 rows containing missing values (geom_point).

## Warning: Removed 645 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1     77     126.36                            
## 2     76     126.07  1 0.2965  0.1787 0.67365  
## 3     75     116.38  1 9.6919  6.2461 0.01463 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 417.9807
## 2     2 419.7928
## 3     3 415.3932

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge    -0.97364    1.75926  -0.553  0.58161   
## phi    0.04865    0.06792   0.716  0.47601   
## alpha  0.92741    0.33424   2.775  0.00697 **
## A     10.48547    4.92727   2.128  0.03662 * 
## k     30.84036   15.66786   1.968  0.05272 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.246 on 75 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 8.084e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1     75     116.38                          
## 2     74     113.61  1 2.76491  1.8009 0.1837
## 3     74     113.44  0 0.00000               
## 4     73     113.37  1 0.07089  0.0456 0.8314
##   model      AIC
## 1     3 415.3932
## 2    3a 415.4696
## 3    3b 415.3527
## 4    3c 417.3027

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)   
## ge    -1.309e+00  1.485e+00  -0.882  0.38072   
## phi    5.148e-02  6.724e-02   0.766  0.44632   
## alpha  8.949e-01  3.344e-01   2.676  0.00917 **
## A      3.181e+01  1.075e+02   0.296  0.76811   
## k      2.536e+03  4.364e+04   0.058  0.95382   
## s      3.345e-01  3.981e-01   0.840  0.40345   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.238 on 74 degrees of freedom
## 
## Number of iterations to convergence: 20 
## Achieved convergence tolerance: 1.797e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88149, p-value = 2.186e-06
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.1089, p-value = 0.2675
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

## Warning: Removed 725 row(s) containing missing values (geom_path).

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)   
## 1   1785     2717.6                               
## 2   1784     2714.0  1  3.6387  2.3919 0.122145   
## 3   1783     2700.9  1 13.0325  8.6033 0.003398 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7661.536
## 2     2 7661.140
## 3     3 7654.534

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.16616    0.50732   0.328  0.74331    
## phi    0.01898    0.01401   1.354  0.17578    
## alpha  0.37133    0.12160   3.054  0.00229 ** 
## A      3.36013    0.32889  10.216  < 2e-16 ***
## k     15.64879    3.31387   4.722 2.52e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.231 on 1783 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 8.748e-06
##   (507 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1783     2700.9                                
## 2   1781     2589.1  2 111.85   38.47 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 7654.534
## 2    3a       NA
## 3    3b       NA
## 4    3c 7582.913

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge     -0.13781    0.43699  -0.315    0.753  
## phi     0.02415    0.01369   1.764    0.078 .
## alpha   0.18907    0.11545   1.638    0.102  
## A       9.65502   15.02288   0.643    0.521  
## k     326.59086  478.82390   0.682    0.495  
## s       2.22000    1.13686   1.953    0.051 .
## p       0.24537    0.39035   0.629    0.530  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.206 on 1781 degrees of freedom
## 
## Number of iterations to convergence: 20 
## Achieved convergence tolerance: 8.752e-06
##   (507 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.72987, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.7932, p-value = 1.097e-11
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 254 rows containing missing values (geom_point).

## Warning: Removed 1176 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Error in nls(fg_1, data = G_255, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit
note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    212     109.50                             
## 2    211     107.99  1 1.5070  2.9444 0.08765 . 
## 3    210     103.86  1 4.1364  8.3639 0.00423 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 506.5831
## 2     2 505.6036
## 3     3 499.2067

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge     -1.60390    0.75643  -2.120  0.03515 * 
## phi    -0.09495    0.07250  -1.310  0.19176   
## alpha   0.82023    0.25228   3.251  0.00134 **
## A       4.22990    1.38936   3.044  0.00263 **
## k     124.24892   42.33717   2.935  0.00371 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7032 on 210 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.944e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_313,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    210    103.856                            
## 2    209    101.102  1 2.7533  5.6916 0.01794 *
## 3    208     98.863  1 2.2389  4.7105 0.03111 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 499.2067
## 2    3a 495.4300
## 3    3b       NA
## 4    3c 492.6153

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.59741    0.73738  -2.166 0.031422 *  
## phi    -0.08343    0.06684  -1.248 0.213356    
## alpha   0.83684    0.24358   3.436 0.000714 ***
## A       3.16355    1.01981   3.102 0.002188 ** 
## k     111.46478   26.09832   4.271 2.96e-05 ***
## s       2.87973    1.34426   2.142 0.033336 *  
## p       0.30573    0.09555   3.200 0.001591 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6894 on 208 degrees of freedom
## 
## Number of iterations to convergence: 20 
## Achieved convergence tolerance: 8.622e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97899, p-value = 0.002688
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.36661, p-value = 0.7139
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1103 row(s) containing missing values (geom_path).

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    193     173.52                            
## 2    192     173.47  1 0.0524  0.0579 0.81003  
## 3    191     168.50  1 4.9689  5.6324 0.01862 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 665.6359
## 2     2 667.5768
## 3     3 663.8805

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge     0.51605    1.63140   0.316  0.75210   
## phi    0.01497    0.03142   0.477  0.63424   
## alpha  0.66415    0.25423   2.612  0.00971 **
## A      3.91042    1.26582   3.089  0.00231 **
## k     57.76819   18.99786   3.041  0.00269 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9393 on 191 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.985e-06
##   (36 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    191     168.50                              
## 2    190     160.32  1 8.1820  9.6969 0.002131 **
## 3    189     158.12  1 2.1996  2.6292 0.106584   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 663.8805
## 2    3a 656.1243
## 3    3b       NA
## 4    3c 655.4165

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge     0.17215    1.38113   0.125  0.90094   
## phi    0.02067    0.03102   0.666  0.50596   
## alpha  0.68028    0.22567   3.014  0.00293 **
## A      3.79683    1.23637   3.071  0.00245 **
## k     84.69132   26.33183   3.216  0.00153 **
## p      0.29323    0.09705   3.021  0.00286 **
## s      2.36410    1.17963   2.004  0.04649 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9147 on 189 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 7.581e-06
##   (36 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91018, p-value = 1.565e-09
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.4234, p-value = 0.1546
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 18 rows containing missing values (geom_point).

## Warning: Removed 1120 row(s) containing missing values (geom_path).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1    112     82.270                               
## 2    111     82.264  1 0.0062  0.0083 0.927546    
## 3    110     74.204  1 8.0592 11.9469 0.000779 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 315.0331
## 2     2 317.0245
## 3     3 307.1674

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.96617    5.50627   0.357 0.721718    
## phi    0.00124    0.05446   0.023 0.981879    
## alpha  0.98497    0.24440   4.030 0.000103 ***
## A      3.26566    2.69600   1.211 0.228376    
## k     82.57910   32.74227   2.522 0.013097 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8213 on 110 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.047e-06
##   (9 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    110     74.204                           
## 2    109     74.164  1 0.040526  0.0596 0.8076
## 3    109     74.195  0 0.000000               
## 4    108     74.158  1 0.036489  0.0531 0.8181
##   model      AIC
## 1     3 307.1674
## 2    3a 309.1046
## 3    3b 309.1521
## 4    3c 311.0955

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.96617    5.50627   0.357 0.721718    
## phi    0.00124    0.05446   0.023 0.981879    
## alpha  0.98497    0.24440   4.030 0.000103 ***
## A      3.26566    2.69600   1.211 0.228376    
## k     82.57910   32.74227   2.522 0.013097 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8213 on 110 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.047e-06
##   (9 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9487, p-value = 0.0002425
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.94042, p-value = 0.347
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).

## Warning: Removed 1241 row(s) containing missing values (geom_path).

plotting 2

411 - Everglades

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6746     5753.1                                
## 2   6745     5726.7  1  26.40  31.097  2.55e-08 ***
## 3   6744     5393.0  1 333.75 417.356 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25694.00
## 2     2 25664.96
## 3     3 25261.71

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.624232   0.198138   3.150  0.00164 ** 
## phi   0.019924   0.004531   4.397 1.11e-05 ***
## alpha 0.637587   0.029038  21.957  < 2e-16 ***
## A     2.999615   0.114078  26.294  < 2e-16 ***
## k     2.752660   0.406438   6.773 1.37e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8942 on 6744 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.222e-06
##   (23 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   6744     5393.0                              
## 2   6743     5389.8  1 3.1997  4.0030 0.045458 * 
## 3   6743     5392.8  0 0.0000                    
## 4   6742     5385.3  1 7.5612  9.4662 0.002101 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 25261.71
## 2    3a 25259.70
## 3    3b 25263.50
## 4    3c 25256.03

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.60999    0.19692   3.098  0.00196 ** 
## phi    0.02012    0.00453   4.441 9.12e-06 ***
## alpha  0.63490    0.02899  21.901  < 2e-16 ***
## A      2.95554    0.11274  26.216  < 2e-16 ***
## k      9.93538    2.30225   4.316 1.62e-05 ***
## p      0.46592    0.07809   5.966 2.55e-09 ***
## s      1.85621    0.46313   4.008 6.19e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8937 on 6742 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 7.419e-06
##   (23 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).

## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   8257      16789                              
## 2   8256      16786  1   2.46   1.2104 0.2713    
## 3   8255      16418  1 368.11 185.0856 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40113.33
## 2     2 40114.12
## 3     3 39932.96

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.020544   0.177726   0.116    0.908    
## phi   -0.004884   0.006639  -0.736    0.462    
## alpha  0.814722   0.056701  14.369  < 2e-16 ***
## A      4.180968   0.157264  26.586  < 2e-16 ***
## k      7.281964   1.424676   5.111 3.27e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.41 on 8255 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 4.273e-06
##   (55 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 39932.96
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.020544   0.177726   0.116    0.908    
## phi   -0.004884   0.006639  -0.736    0.462    
## alpha  0.814722   0.056701  14.369  < 2e-16 ***
## A      4.180968   0.157264  26.586  < 2e-16 ***
## k      7.281964   1.424676   5.111 3.27e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.41 on 8255 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 4.273e-06
##   (55 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 27 rows containing missing values (geom_point).

## Warning: Removed 982 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    887     1339.4                                
## 2    886     1339.3  1  0.140  0.0923    0.7613    
## 3    885     1292.8  1 46.501 31.8328 2.261e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3727.581
## 2     2 3729.488
## 3     3 3700.038

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.61273    1.92481   1.877   0.0609 .  
## phi   -0.01887    0.02481  -0.761   0.4471    
## alpha  0.92667    0.15103   6.136 1.28e-09 ***
## A      1.67614    0.38072   4.402 1.20e-05 ***
## k      3.83833    3.27829   1.171   0.2420    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.209 on 885 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 4.701e-06
##   (6 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 3700.038
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.61273    1.92481   1.877   0.0609 .  
## phi   -0.01887    0.02481  -0.761   0.4471    
## alpha  0.92667    0.15103   6.136 1.28e-09 ***
## A      1.67614    0.38072   4.402 1.20e-05 ***
## k      3.83833    3.27829   1.171   0.2420    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.209 on 885 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 4.701e-06
##   (6 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94516, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.1788, p-value = 0.02935
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).

## Warning: Removed 1175 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    989     1487.8                                
## 2    988     1466.1  1 21.624  14.572 0.0001433 ***
## 3    987     1403.8  1 62.340  43.831 5.869e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4215.211
## 2     2 4202.687
## 3     3 4161.584

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.64775    1.69266   1.564  0.11808    
## phi    0.07074    0.02643   2.677  0.00756 ** 
## alpha  0.76844    0.10741   7.154 1.64e-12 ***
## A      1.83534    0.41750   4.396 1.22e-05 ***
## k      1.60048    0.96067   1.666  0.09603 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.193 on 987 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 7.134e-06
##   (14 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 4161.584
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.64775    1.69266   1.564  0.11808    
## phi    0.07074    0.02643   2.677  0.00756 ** 
## alpha  0.76844    0.10741   7.154 1.64e-12 ***
## A      1.83534    0.41750   4.396 1.22e-05 ***
## k      1.60048    0.96067   1.666  0.09603 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.193 on 987 degrees of freedom
## 
## Number of iterations to convergence: 17 
## Achieved convergence tolerance: 7.134e-06
##   (14 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95429, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.4242, p-value = 5.823e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

## Warning: Removed 1218 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value  Pr(>F)    
## 1   3147     8417.1                               
## 2   3146     8404.1  1  12.96   4.8528 0.02767 *  
## 3   3145     8007.1  1 397.02 155.9417 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 16149.88
## 2     2 16147.03
## 3     3 15996.59

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.64015    0.24959  -6.571 5.81e-11 ***
## phi    -0.02633    0.01749  -1.505    0.132    
## alpha   0.96541    0.06969  13.854  < 2e-16 ***
## A      12.37097    1.06955  11.567  < 2e-16 ***
## k     128.53784   10.22671  12.569  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.596 on 3145 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.151e-06
##   (74 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   3145     8007.1                                 
## 2   3144     7892.5  1 114.589  45.647 1.681e-11 ***
## 3   3144     7925.1  0   0.000                      
## 4   3143     7880.2  1  44.853  17.889 2.408e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 15996.59
## 2    3a 15953.18
## 3    3b 15966.16
## 4    3c 15950.28

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.63573    0.24760  -6.606 4.61e-11 ***
## phi    -0.02333    0.01726  -1.352    0.176    
## alpha   0.93860    0.07003  13.403  < 2e-16 ***
## A      11.22362    1.11339  10.081  < 2e-16 ***
## k     166.50196   18.41444   9.042  < 2e-16 ***
## p       0.20777    0.02940   7.068 1.93e-12 ***
## s       1.65252    0.23988   6.889 6.76e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.583 on 3143 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.027e-06
##   (74 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92449, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.9781, p-value = 6.423e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 39 rows containing missing values (geom_point).

## Warning: Removed 126 row(s) containing missing values (geom_path).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1682     3723.6                                 
## 2   1681     3593.1  1 130.459  61.034 9.807e-15 ***
## 3   1680     3507.6  1  85.504  40.953 2.017e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7999.216
## 2     2 7941.121
## 3     3 7902.539

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.55370    0.36681  -4.236 2.40e-05 ***
## phi     0.16330    0.01741   9.382  < 2e-16 ***
## alpha   0.72152    0.10445   6.908 6.95e-12 ***
## A      15.71695    1.85052   8.493  < 2e-16 ***
## k     183.91121   21.84212   8.420  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.445 on 1680 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.978e-06
##   (292 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1680     3507.6                                
## 2   1679     3472.9  1 34.721  16.786 4.383e-05 ***
## 3   1679     3492.3  0  0.000                      
## 4   1678     3469.0  1 23.332  11.286 0.0007985 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 7902.539
## 2    3a 7887.776
## 3    3b 7897.190
## 4    3c 7887.895

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.57373    0.35934  -4.380 1.26e-05 ***
## phi     0.16399    0.01724   9.511  < 2e-16 ***
## alpha   0.70751    0.10290   6.876 8.66e-12 ***
## A      19.41660    2.88667   6.726 2.38e-11 ***
## k     340.27521   77.07101   4.415 1.07e-05 ***
## p       0.06498    0.01245   5.221 2.00e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.438 on 1679 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 2.647e-06
##   (292 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89406, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.082746, p-value = 0.9341
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 155 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    363     173.85                                 
## 2    362     167.67  1  6.1874  13.359 0.0002952 ***
## 3    361     151.94  1 15.7225  37.355 2.554e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 867.4285
## 2     2 856.1651
## 3     3 822.1268

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -2.06635    0.35148  -5.879 9.40e-09 ***
## phi     0.06118    0.02220   2.757  0.00614 ** 
## alpha   0.78833    0.11296   6.979 1.43e-11 ***
## A      10.63664    2.05685   5.171 3.86e-07 ***
## k     160.22129   38.00285   4.216 3.15e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6488 on 361 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.837e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M313,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    361     151.94                          
## 2    360     151.06  1 0.88856  2.1176 0.1465
##   model      AIC
## 1     3 822.1268
## 2    3a 821.9802
## 3    3b 821.6317
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -2.057e+00  3.537e-01  -5.815 1.34e-08 ***
## phi    6.070e-02  2.224e-02   2.729 0.006668 ** 
## alpha  7.848e-01  1.131e-01   6.942 1.81e-11 ***
## A      5.415e+01  1.907e+02   0.284 0.776569    
## k      3.935e+03  2.527e+04   0.156 0.876316    
## s      6.923e-01  1.775e-01   3.900 0.000115 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6475 on 360 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 8.299e-07
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97137, p-value = 1.275e-06
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.47103, p-value = 0.6376
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1183 row(s) containing missing values (geom_path).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1732     1567.7                                
## 2   1731     1548.6  1  19.07  21.316 4.182e-06 ***
## 3   1730     1445.7  1 102.91 123.143 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4946.994
## 2     2 4927.760
## 3     3 4810.458

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.48851    0.66592  -0.734    0.463    
## phi    0.09081    0.01449   6.266 4.68e-10 ***
## alpha  0.72031    0.05452  13.212  < 2e-16 ***
## A      2.58293    0.43178   5.982 2.67e-09 ***
## k     37.69903    6.08368   6.197 7.19e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9141 on 1730 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.369e-06
##   (21 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M331,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1730     1445.7                                
## 2   1729     1415.8  1 29.836  36.435 1.927e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 4810.458
## 2    3a 4776.276
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.22164    0.74109  -0.299   0.7649    
## phi     0.09382    0.01430   6.562 7.01e-11 ***
## alpha   0.73135    0.05290  13.824  < 2e-16 ***
## A       7.18085    4.09409   1.754   0.0796 .  
## k     612.34714  500.06592   1.225   0.2209    
## p       0.11073    0.05384   2.057   0.0399 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9049 on 1729 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.434e-06
##   (21 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.8548, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.414, p-value = 1.015e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

## Warning: Removed 1091 row(s) containing missing values (geom_path).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   2513     2864.1                                
## 2   2512     2859.8  1   4.302   3.7787 0.05202 .  
## 3   2511     2603.5  1 256.310 247.2055 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8728.807
## 2     2 8727.025
## 3     3 8492.774

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.91771    0.42327  -2.168   0.0302 *  
## phi    0.02631    0.01737   1.515   0.1300    
## alpha  0.90510    0.04945  18.302  < 2e-16 ***
## A      4.94379    0.62849   7.866 5.39e-15 ***
## k     64.39021    7.07215   9.105  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.018 on 2511 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 9.236e-06
##   (96 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   2511     2603.5                               
## 2   2510     2491.6  1 111.878 112.7038 <2e-16 ***
## 3   2509     2491.2  1   0.432   0.4356 0.5093    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 8492.774
## 2    3a 8384.264
## 3    3b       NA
## 4    3c 8385.827

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.96761    0.39955  -2.422  0.01552 *  
## phi     0.02091    0.01696   1.233  0.21760    
## alpha   0.88857    0.04853  18.310  < 2e-16 ***
## A      15.40333    5.95451   2.587  0.00974 ** 
## k     760.03188  384.19799   1.978  0.04801 *  
## p       0.07577    0.02482   3.053  0.00229 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9963 on 2510 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.075e-06
##   (96 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90479, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.0048, p-value = 2.473e-12
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 46 rows containing missing values (geom_point).

## Warning: Removed 1001 row(s) containing missing values (geom_path).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   1691     2122.4                               
## 2   1690     2120.4  1   2.008   1.6001 0.2061    
## 3   1689     1851.2  1 269.153 245.5647 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6712.211
## 2     2 6712.608
## 3     3 6484.655

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.58199    0.57724  -1.008    0.313    
## phi    0.00104    0.01880   0.055    0.956    
## alpha  0.94886    0.05266  18.017  < 2e-16 ***
## A      5.54606    0.82458   6.726 2.38e-11 ***
## k     44.21369    4.89817   9.027  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.047 on 1689 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.004e-06
##   (59 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M333,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M333,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1689     1851.2                                
## 2   1688     1754.0  1 97.241  93.582 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6484.655
## 2    3a 6395.251
## 3    3b       NA
## 4    3c       NA

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.670171   0.536892  -1.248 0.212115    
## phi     0.006873   0.018253   0.377 0.706553    
## alpha   0.930227   0.050682  18.354  < 2e-16 ***
## A      13.343494   3.465477   3.850 0.000122 ***
## k     466.537719 163.579207   2.852 0.004397 ** 
## p       0.114498   0.020826   5.498 4.43e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.019 on 1688 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 2.994e-06
##   (59 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93155, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6597, p-value = 3.167e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 29 rows containing missing values (geom_point).

## Warning: Removed 925 row(s) containing missing values (geom_path).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    355     353.04                                 
## 2    354     353.04  1  0.0053  0.0053    0.9422    
## 3    353     326.43  1 26.6098 28.7760 1.473e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1090.416
## 2     2 1092.410
## 3     3 1066.355

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.13825    3.71884   0.575  0.56567    
## phi   -0.03467    0.03674  -0.944  0.34601    
## alpha  0.81562    0.13184   6.186  1.7e-09 ***
## A      1.66966    0.86432   1.932  0.05419 .  
## k     29.26846    9.25921   3.161  0.00171 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9616 on 353 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.954e-06
##   (101 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    353     326.43                          
## 2    352     326.35  1 0.07658  0.0826 0.7740
## 3    352     326.42  0 0.00000               
## 4    351     325.72  1 0.69849  0.7527 0.3862
##   model      AIC
## 1     3 1066.355
## 2    3a 1068.271
## 3    3b 1068.347
## 4    3c 1069.580

## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.13825    3.71884   0.575  0.56567    
## phi   -0.03467    0.03674  -0.944  0.34601    
## alpha  0.81562    0.13184   6.186  1.7e-09 ***
## A      1.66966    0.86432   1.932  0.05419 .  
## k     29.26846    9.25921   3.161  0.00171 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9616 on 353 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.954e-06
##   (101 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.83081, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.3928, p-value = 0.01672
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 48 rows containing missing values (geom_point).

## Warning: Removed 1264 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

Fitted parameters

Best / selected models by ecoprovince

Code	Ecoregion	Sel.Mod
211	Northeastern Mixed Forest	3a
212	Laurentian Mixed Forest	3c
221	Eastern Broadleaf Forest	3a
222	Midwest Broadleaf Forest	3a
223	Central Interior Broadleaf Forest	3
231	Southeastern Mixed Forest	3a
232	Outer Coastal Plain Mixed Forest	3a
234	Lower Mississippi Riverine Forest	3
242	Pacific Lowland Mixed Forest	3b
251	Prairie Parkland (Temperate)	3c
255	Prairie Parkland (Subtropical)	NA
261	California Coastal Chaparral Forest and Shrub	NA
262	California Dry Steppe	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	NA
313	Colorado Plateau Semi-Desert	3c
315	Southwest Plateau and Plains Dry Steppe and Shrub	NA
321	Chihuahuan Semi-Desert	NA
322	American Semidesert and Desert	NA
331	Great Plains/Palouse Dry Steppe	NA
332	Great Plains Steppe	3c
341	Intermountain Semi-Desert and Desert	NA
342	Intermountain Semi-Desert	3
411	Everglades	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	3c
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	3
M223	Ozark Broadleaf Forest Meadow	3
M231	Ouachita Mixed Forest	3
M242	Cascade Mixed Forest	3c
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	3a
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	3b
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	3a
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	3a
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	3a
M334	Black Hills Coniferous Forest	3
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	NA

table by ecoprovince

Code	Ecoregion	region	n.obs	n.plots	ge	ge.variance	ge.2.5	ge.97.5	phi	phi.variance	phi.2.5	phi.97.5	alpha	alpha.variance	alpha.2.5	alpha.97.5	A	A.2.5	A.97.5	k	k.2.5	k.97.5
211	Northeastern Mixed Forest	east	6877	2876	-0.0109798	0.0271725	-0.3341190	0.3121593	0.0201397	0.0000255	0.0102465	0.0300329	0.6327874	0.0011455	0.5664398	0.6991349	3.649991	3.4014689	3.898513	11.607027	6.637676e+00	16.576378
212	Laurentian Mixed Forest	east	22715	9499	0.9543179	0.0255622	0.6409350	1.2677008	0.0264340	0.0000098	0.0203104	0.0325575	0.7992242	0.0004750	0.7565030	0.8419454	2.982149	2.6858766	3.278421	25.323669	1.956755e+01	31.079791
221	Eastern Broadleaf Forest	east	7333	3571	-0.9918148	0.0147550	-1.2299315	-0.7536982	0.0204655	0.0000295	0.0098185	0.0311126	0.7458855	0.0015351	0.6690800	0.8226910	7.709358	6.0816742	9.337041	215.668276	6.760192e+01	363.734636
222	Midwest Broadleaf Forest	east	5845	2589	-0.2014342	0.0524564	-0.6504441	0.2475757	0.0172135	0.0000819	-0.0005251	0.0349522	0.7565621	0.0020782	0.6671896	0.8459346	6.225883	5.2542798	7.197486	125.317993	7.557097e+01	175.065015
223	Central Interior Broadleaf Forest	east	10010	3864	-0.6785951	0.0187709	-0.9471607	-0.4100296	-0.0123567	0.0000444	-0.0254161	0.0007028	0.6675588	0.0018373	0.5835355	0.7515820	4.813998	4.4856269	5.142368	27.676460	2.287080e+01	32.482119
231	Southeastern Mixed Forest	east	13517	6193	1.0486648	0.0285670	0.7173659	1.3799636	0.0051558	0.0000209	-0.0038035	0.0141151	0.8688863	0.0004222	0.8286110	0.9091615	4.439114	4.1813147	4.696913	7.625377	3.215974e+00	12.034780
232	Outer Coastal Plain Mixed Forest	east	13629	6626	0.6998205	0.0284781	0.3690375	1.0306036	0.0046285	0.0000229	-0.0047556	0.0140125	0.8653484	0.0003950	0.8263934	0.9043033	4.879788	4.5515323	5.208044	24.840494	1.701546e+01	32.665527
234	Lower Mississippi Riverine Forest	east	1388	778	1.9080853	1.6699841	-0.6270554	4.4432259	-0.0237106	0.0004721	-0.0663363	0.0189152	0.8045919	0.0067133	0.6438550	0.9653287	3.546196	2.2120751	4.880317	4.451952	1.367813e+00	7.536091
242	Pacific Lowland Mixed Forest	pacific	83	83	-1.3094645	2.2049734	-4.2682228	1.6492938	0.0514806	0.0045209	-0.0824926	0.1854538	0.8948735	0.1118244	0.2285640	1.5611830	31.807945	-182.3604934	245.976384	2535.570834	-8.442068e+04	89491.824379
251	Prairie Parkland (Temperate)	east	2295	906	-0.1378060	0.1909590	-0.9948703	0.7192584	0.0241500	0.0001875	-0.0027081	0.0510081	0.1890667	0.0133288	-0.0373654	0.4154989	9.655022	-19.8093113	39.119354	326.590858	-6.125250e+02	1265.706671
255	Prairie Parkland (Subtropical)	east	717	319	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
261	California Coastal Chaparral Forest and Shrub	pacific	25	25	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
262	California Dry Steppe	pacific	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	pacific	163	161	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
313	Colorado Plateau Semi-Desert	interior west	218	218	-1.5974077	0.5437229	-3.0510957	-0.1437198	-0.0834260	0.0044671	-0.2151894	0.0483374	0.8368358	0.0593329	0.3566271	1.3170445	3.163546	1.1530601	5.174031	111.464778	6.001365e+01	162.915911
315	Southwest Plateau and Plains Dry Steppe and Shrub	interior west	4	4	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
321	Chihuahuan Semi-Desert	interior west	9	9	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
322	American Semidesert and Desert	interior west	3	3	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	interior west	331	255	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
332	Great Plains Steppe	interior west	232	128	0.1721477	1.9075230	-2.5522646	2.8965600	0.0206740	0.0009624	-0.0405219	0.0818700	0.6802818	0.0509272	0.2351253	1.1254384	3.796826	1.3579755	6.235677	84.691316	3.274928e+01	136.633353
341	Intermountain Semi-Desert and Desert	interior west	66	64	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
342	Intermountain Semi-Desert	interior west	124	123	1.9661658	30.3190383	-8.9459742	12.8783057	0.0012399	0.0029665	-0.1066972	0.1091770	0.9849740	0.0597331	0.5006233	1.4693246	3.265664	-2.0771713	8.608500	82.579097	1.769160e+01	147.466598
411	Everglades	east	96	63	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	east	6772	3006	0.6099912	0.0387780	0.2239634	0.9960191	0.0201180	0.0000205	0.0112368	0.0289992	0.6348976	0.0008404	0.5780693	0.6917259	2.955542	2.7345424	3.176542	9.935383	5.422256e+00	14.448511
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	east	8315	3810	0.0205444	0.0315866	-0.3278434	0.3689322	-0.0048836	0.0000441	-0.0178978	0.0081307	0.8147216	0.0032150	0.7035727	0.9258705	4.180968	3.8726905	4.489246	7.281964	4.489240e+00	10.074688
M223	Ozark Broadleaf Forest Meadow	east	896	349	3.6127264	3.7049024	-0.1650029	7.3904556	-0.0188729	0.0006156	-0.0675679	0.0298222	0.9266739	0.0228087	0.6302641	1.2230837	1.676141	0.9289120	2.423370	3.838332	-2.595798e+00	10.272462
M231	Ouachita Mixed Forest	east	1006	495	2.6477547	2.8650948	-0.6738694	5.9693788	0.0707385	0.0006985	0.0188744	0.1226026	0.7684380	0.0115370	0.5576591	0.9792169	1.835343	1.0160634	2.654623	1.600476	-2.847238e-01	3.485676
M242	Cascade Mixed Forest	pacific	3224	3207	-1.6357285	0.0613078	-2.1212104	-1.1502465	-0.0233320	0.0002978	-0.0571692	0.0105052	0.9385960	0.0049041	0.8012878	1.0759041	11.223621	9.0405696	13.406671	166.501965	1.303964e+02	202.607509
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	pacific	1977	1807	-1.5737277	0.1291222	-2.2785210	-0.8689343	0.1639934	0.0002973	0.1301737	0.1978132	0.7075065	0.0105879	0.5056853	0.9093277	19.416604	13.7547440	25.078464	340.275212	1.891098e+02	491.440588
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	interior west	30	26	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	367	367	-2.0566556	0.1250833	-2.7521765	-1.3611346	0.0606986	0.0004948	0.0169552	0.1044421	0.7848411	0.0127830	0.5624961	1.0071860	54.151313	-320.8143982	429.117024	3935.373875	-4.575415e+04	53624.896968
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	1756	1756	-0.2216358	0.5492199	-1.6751703	1.2318986	0.0938226	0.0002045	0.0657782	0.1218671	0.7313497	0.0027987	0.6275896	0.8351097	7.180848	-0.8490325	15.210729	612.347135	-3.684506e+02	1593.144911
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	2612	2602	-0.9676071	0.1596412	-1.7510910	-0.1841233	0.0209145	0.0002876	-0.0123404	0.0541694	0.8885691	0.0023551	0.7934078	0.9837304	15.403326	3.7270718	27.079581	760.031876	6.654360e+00	1513.409391
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	1753	1742	-0.6701713	0.2882529	-1.7232151	0.3828726	0.0068732	0.0003332	-0.0289277	0.0426742	0.9302266	0.0025687	0.8308201	1.0296332	13.343494	6.5464106	20.140578	466.537719	1.456983e+02	787.377126
M334	Black Hills Coniferous Forest	interior west	459	181	2.1382508	13.8297772	-5.1756196	9.4521211	-0.0346717	0.0013501	-0.1069349	0.0375915	0.8156215	0.0173818	0.5563309	1.0749121	1.669664	-0.0302026	3.369531	29.268462	1.105831e+01	47.478618
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	interior west	220	220	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

## Warning: package 'ggnewscale' was built under R version 4.2.1

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 14 rows containing missing values (geom_point).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 14 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1     entire US  0.11390352            0.06580423    0.242879814    -0.01507276
## 2       pacific -0.14153116            0.01783556   -0.106573459    -0.17648887
## 3          east  0.33357842            0.05129085    0.434108486     0.23304835
## 4 interior west -0.07814373            0.03716635   -0.005297675    -0.15098978

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US  0.016793959            0.002045228    0.020802607
## 2       pacific  0.003897856            0.001100690    0.006055209
## 3          east  0.008895102            0.001336975    0.011515572
## 4 interior west  0.004001002            0.001088090    0.006133657
##   95 % CI, lower
## 1    0.012785312
## 2    0.001740503
## 3    0.006274631
## 4    0.001868346

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.77078681              0.010164810     0.79070984
## 2       pacific     0.07531836              0.005056256     0.08522862
## 3          east     0.59114245              0.008128291     0.60707390
## 4 interior west     0.10432600              0.003418849     0.11102695
##   95 % CI, lower
## 1     0.75086378
## 2     0.06540810
## 3     0.57521100
## 4     0.09762506

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   6.389644
## 2       pacific  13.954195
## 3          east   4.421361
## 4 interior west  12.689849

K (stand biomass at half biomass G in Mg/ha)

##          region weighted.k
## 1     entire US  151.33635
## 2       pacific  257.29727
## 3          east   45.53192
## 4 interior west  696.34581

FIA NLS Models: Biomass Growth vs. Biomass

JAH

2022-12-14

Background

211 - Northeastern Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

summary

model selection 2